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theory. Since, then, there is only a change of one-thousandth 
in the length of the column, it is quite obvious that the amount 
of effect produced upon the column of mercury in the Challenger 
thermometers (which is not above a sixth or a seventh of a metre 
in length at the utmost), that is to say, the whole correction- 
difference between the maximum and minimum indices is a 
matter of a sixth or seventh of a millimetre ; or in general very 
nearly the same fraction of a degree of the scale. Thus it is 
proved that the correction supplied by the Admiralty, if it is to 
be applied at all, ought to be applied almost in its entirety to the 
minimum index, 
VIII. Zhe Aneurisms. Their Object and Effects.—There is 
another peculiarity of the Challenger thermometers, which leads 
to a slight—but only a slight—modification of this statement, 
viz. that at the lower end of each of the two vertical columns 
there is ananeurism on the tube. These form a sort of secondary 
bulb, making the tube faulty again after the primary bulb has 
been protected. Their effect is slightly to increase the effective 
length of the column of mercury. 
I learned from Sir George Nares that the object of these 
aneurisms, and of another which is situated close to the bulb, is 
to prevent the indices from being jammed at the bends of the 
stem, or forced into the bulb, when the instrument is expo ed to 
very high or very low temperatures. ‘[hey seem to be in every 
respect objectionable, especially as the necessity for them would 
be entirely removed by adding an inch or two to the length of 
the instrument ; or, if they must be retained, by protecting them 
and using more powerful magnets. Their presence produces an 
effect large compared with their apparent importance. The 
sketch below represents, on a large scale, one of the most highly 
developed of the more effective of these aneurisms, that which is 
situated close to the main bulb of the instrument. 
Kaa. 0 
Fic. 1.—'The chief Aneurism. 
Y 
By reason of the convexity of the thermometer tube the dia- 
meter of the bore appears from the outside to be considerably 
larger than it really is. In fact a very simple geometrical con- 
struction shows that the ratio of its apparent diameter to its real 
diameter is that of the refractive index of glass to unity, ze. it 
appears to be about 1°6 times its actual diameter. So that even 
when the aneurism, and the liquid filling it, appear to occupy 
the whole diameter of the tube, they only occupy =% or about 
two-thirds, so that even in this extreme case the walls of the 
aneurism are not usually very thin. The percentage diminution 
of volume of the middle portion of the aneurism is in such a 
st (roughly) 50 per cent. greater than that of the unaltered 
tube. 
The real mischief done by the aneurism is not due mainly to 
thinness of the walls and consequent greater liability to distor- 
tion by pressure ; it is due to the fact that the aneurism, in con- 
sequence of its greater section, contains a much larger quantity 
of mercury than does an equal length of the tube; and there- 
fore that a small percentage diminution of its volume will pro- 
duce a marked displacement by the outflow into the narrow tube. 
Several of the aneurisms I have measured produce a disturbance 
of the index corresponding to that produced by at least five times 
their own length of the tube. 
In some of the more exaggerated ones it actually produces an 
effect on the maximum and minimum index equal to that due to 
the extension of yery nearly one-half of the mercury column in 
the thermometer, But this, though easily remediable, is not a 
defect of much consequence. 
IX. Imploding and Exploding of the Thermometer Bulbs.— 
In comection with the breaking of some of the thermometers, 
as a result of pressure whether in the press or in the sea, it may 
be well to describe the curious nature of the effects produced by 
pressure upon the material of a tube, according as the pressure 
is applied from without or from within. 
First, with regard to the thermometers themselves, which are 
exposed to external pressure, but have comparatively very slight — 
pressure applied in the interior of their bore ; and second, the — 
corresponding effect when pressure is applied, as in the press 
itself, from the inside and tends to stretch the walls. [This 
second case has occurred with one or two of the Challenger 
thermometers also. Its source is usually defective strength of 
the terminal bulb of the maximum end of the tube. This bulb. 
implodes, then the pressure is applied to the interior of the 
protected bulb, which, inits turn, explodes.] 
In the diagrams below, the first three figures refer to part 
of the walls of the glass tube, which is exposed to pressure from. 
the outside, but has no corresponding pressure applied within, 
es 
Fic. 2.—Distortion due to external pressure. 
The effects of pressure indicated are those in a transverse sec- 
tion of the tube. The circles represent (on a large scale) transverse 
sections of very small spherical elements of the glass wall of the 
tube, the first close to the outside, the second in the middle of the 
wall of the tube, and the third close to the inner surface, The 
ellipses which are drawn along with the circles represent (of 
course, with much exaggeration) the corresponding transverse 
sections of the ellipsoids into which the spheres are distorted by, 
the external pressure, The sphere near the outside is compressed 
in all directions, but much less in a radial direction than it is in 
a direction perpendicular to the former. The greatest amount 
of compression is tangential as it were, and the circular section 
of the sphere has been compressed into an ellipse which has a 
major axis in the radial direction very nearly equal to its original 
length, while the minor axis is very considerably reduced. The 
second figure refers to a small spherical portion inside the glass 
wall originally situated at a distance from the axis equal to 1°6. 
times the internal radius of the tube. (It is curious that the 
number 1°6, though obtained from a totally different source, 
should be so nearly the same as that already quoted as the 
refractive index of the glass.) The little spherical element at 
that place suffers no radial compression, but there is considerable 
tangential compression. Close to the interior surface of the 
glass tube we find large compression in a tangential direction 
and actual extension in the radial direction. These diagrams 
have been purposely exaggerated to make the effects visible. 
They represent what would be the effect of a pressure of 650 
tons weight per square inch, provided glass could stand such a. 
pressure and still continued to follow Hooke’s law ; and the outer 
radius of the tube has been taken as 2°2 times the inner. But 
they give all that is really required, viz. the character of the 
distortion at different points in the wall of the tube. 
The next three figures represent the corresponding changes in 
ae 
Fic. 3.—Distortion due to internal pressure. 
spherical elements of the same cylindrical tube exposed to pres- 
sure from within. All portions of the tube are now extended’ 
tangentially and compressed radially, but the amount is greater 
on each layer as it is nearer the interior surface. 
It is now easy to see how it is that a glass tube is broken by 
the application of pressure from without. The effect is, of course, 
produced first at the interior surface. For the compression is 
the same for every portion of the glass, but it is accompanied 
by shear, which increases towards the inner surface ; and it is 
